Question: Simplify the following expression: $a = \dfrac{18n^2}{-18n^2 + 39n}$ You can assume $n \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $18n^2 = (2\cdot3\cdot3 \cdot n \cdot n)$ The denominator can be factored: $-18n^2 + 39n = - (2\cdot3\cdot3 \cdot n \cdot n) + (3\cdot13 \cdot n)$ The greatest common factor of all the terms is $3n$ Factoring out $3n$ gives us: $a = \dfrac{(3n)(6n)}{(3n)(-6n + 13)}$ Dividing both the numerator and denominator by $3n$ gives: $a = \dfrac{6n}{-6n + 13}$